A \( x^{2} + y^{2} + 2 y - 2 y = 52 \)
B \( x^{2} + y^{2} - 2 x + 2 y = 62 \)
C \( x^{2} + y^{2} - 2 x + 2 y = 47 \)
D \( x^{2} + y^{2} + 2 x - 2 y = 62 \)
Correct Answer: Option C
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